Study on the Location of Small Reservoir in Hilly Area by Newton Method

Chi, Xiaoli; Chi, Enxian; Tang, Chunhua

doi:10.1088/1742-6596/1574/1/012137

Cited by 1 publication

(2 citation statements)

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“…For bounded and continuous response surfaces, this step can be used to evaluate and identify the critical points as extreme points, and the corresponding maximum/minimum values are frequently achieved at extreme points and endpoints. Terefore, instead of considering the critical points in the global domain, an iterative method known as the Newton iteration method [44] is directly applied to solve the extreme points. Te boundary extreme points are estimated based on the boundary domain generated under various situations.…”

Section: Newton Iteration Methods For the Calculation Of Globalmentioning

confidence: 99%

“…Based on this idea, the response surface is frst constructed by MAAOP, after which the global scope of the response surface's monotonicity is examined. Subsequently, the Newton iteration method [44] is introduced for the calculation of global extreme points, while a transformation boundary method is developed for the calculation of boundary extreme points, all based on the results of the monotonicity analysis. Te detailed procedure of RSO-ETM will be deduced in the next subsections.…”

Section: Rso-etm For Uncertainty Analysis With Epistemic Uncertaintiesmentioning

confidence: 99%

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Reduced Space Optimization‐Based Evidence Theory Method for Response Analysis of Space‐Coiled Acoustic Metamaterials with Epistemic Uncertainty

Yin

Chen

Qin

2023

Mathematical Problems in Engineering

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Acoustic metamaterials have been widely concerned by researchers because of their excellent sound absorption properties. Traditional uncertainty analysis methods for response analysis of acoustic metamaterials with evidence variables have limitations. The excessive time spent on repetitive extreme analysis of focal elements severely impedes the practical application of evidence theory. To reduce the computational costs of uncertainty quantification for acoustic metamaterials under the evidence theory, a reduced space optimization-based evidence theory method (RSO-ETM) is proposed. In RSO-ETM, a simplified surrogate model is first constructed by a modified adaptive arbitrary orthogonal polynomial (MAAOP) expansion method, and then, the monotonicity of the response surface is examined to reduce the space. Subsequently, the Newton iteration technique and a transformation boundary method are used to obtain the extreme points in the reduced space, through which the boundary of the response over each focal element can be readily obtained. By using RSO-ETM, the optimization for each focal element can be avoided, and correspondingly the computational costs are reduced. Two mathematical examples and acoustic problems are employed to demonstrate the practicality of the methods.

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Section: Newton Iteration Methods For the Calculation Of Globalmentioning

confidence: 99%

Section: Rso-etm For Uncertainty Analysis With Epistemic Uncertaintiesmentioning

confidence: 99%